We construct(modified)scattering operators for the Vlasov-Poisson system in three dimensions,mapping small asymptotic dynamics as t→−∞to asymptotic dynamics as t→+∞.The main novelty is the construction of modified...We construct(modified)scattering operators for the Vlasov-Poisson system in three dimensions,mapping small asymptotic dynamics as t→−∞to asymptotic dynamics as t→+∞.The main novelty is the construction of modified wave operators,but we also obtain a new simple proof of modified scattering.Our analysis is guided by the Hamiltonian structure of the Vlasov-Poisson system.Via a pseudo-conformal inversion,we recast the question of asymptotic behavior in terms of local in time dynamics of a new equation with singular coefficients which is approximately integrated using a generating function.展开更多
Within a Pekeris-type approximation to the centrifugal term, we examine the approximately analytical scattering state solutions of the l-wave Schrdinger equation with the modified Rosen–Morse potential. The calculati...Within a Pekeris-type approximation to the centrifugal term, we examine the approximately analytical scattering state solutions of the l-wave Schrdinger equation with the modified Rosen–Morse potential. The calculation formula of phase shifts is derived, and the corresponding bound state energy levels are also obtained from the poles of the scattering amplitude.展开更多
In this paper we consider a coupled Wave-Klein–Gordon system in 3 D, and prove global regularity and modified scattering for small and smooth initial data with suitable decay at infinity. This system was derived by W...In this paper we consider a coupled Wave-Klein–Gordon system in 3 D, and prove global regularity and modified scattering for small and smooth initial data with suitable decay at infinity. This system was derived by Wang and LeFloch–Ma as a simplified model for the global nonlinear stability of the Minkowski space-time for self-gravitating massive fields.展开更多
Some difficulties are pointed out in the methods for identification of obstacles based on the numerical verification of tile inclusion of a function in the range of an operator. Numerical examples are given to illustr...Some difficulties are pointed out in the methods for identification of obstacles based on the numerical verification of tile inclusion of a function in the range of an operator. Numerical examples are given to illustrate theoretical conclusions. Alternative methods of identification of obstacles are mentioned： the Support Function Method （SFM） and the Modified Rayleigh Conjecture （MRC） method.展开更多
This paper investigates in detail the dynamics of the modified KdV equation with self-consistent sources, including characteristics of one-soliton, scattering conditions and phase shifts of two solitons, degenerate ca...This paper investigates in detail the dynamics of the modified KdV equation with self-consistent sources, including characteristics of one-soliton, scattering conditions and phase shifts of two solitons, degenerate case of two solitons and ＂ghost＂ solitons, etc. Co-moving coordinate frames are employed in asymptotic analysis.展开更多
To get the scattering loss of the trapezoidal core waveguide,a new analysis model is presented based on the perturbation equivalent method and modified effective-index method.Firstly,the trapezoidal core waveguide is ...To get the scattering loss of the trapezoidal core waveguide,a new analysis model is presented based on the perturbation equivalent method and modified effective-index method.Firstly,the trapezoidal core waveguide is successfully equivalent to the rectangular one with both restricting the same optical field energy by adopting the perturbation method,Then,the equivalent rectangular core waveguide is decomposed into two slab waveguides by employing the modified effective-index method,The trapezoidal core waveguide scattering theory model is established based on the slab waveguide scattering theory.With the sidewalls surface roughness in the range from 0 to 100 nm in the single model trapezodial core waveguide,optical simulation shows excellent agreement with the results from the scattering loss model presented.The relationship between the dimension and side-wall roughness with the scattering loss can be determined in the trapezoidal core waveguide by the scattering loss model.展开更多
The small nanosilver was prepared by the sodium borohydride procedure. The aptamer was used to modify nanosilver to obtain a nanosilver-aptamer （AgssDNA） SERS probe for the determination of melamine. In pH 6.6 phosp...The small nanosilver was prepared by the sodium borohydride procedure. The aptamer was used to modify nanosilver to obtain a nanosilver-aptamer （AgssDNA） SERS probe for the determination of melamine. In pH 6.6 phosphate buffer solution and in the presence of NaCI, the AgssDNA probe specifically combined with melamine to release nanosilver particles that were aggregated to nanosilver clusters, which exhibited SERS effect at 240 cm-1. When melamine concentration increased, the nanosilver clusters increased, and the SERS intensity at 240 cm-1 in- creased. The increased SERS intensity AI240cm, is linear to melamine concentration in the range of 6.3--403.6 μg.L 1, with a detection limit of 1.2 μg L 1. This assay was applied to determination of melamine in milk, with sat- isfactory results. Keywords melamine, apatmer-modified nanosilver, aggregation, surface-enhanced Raman scattering展开更多
Criticality problem of nuclear tractors generMly refers to an eigenvalue problem for the transport equations. In this paper, we deal with the eigenvalue of the anisotropic scattering transport equation in slab geometr...Criticality problem of nuclear tractors generMly refers to an eigenvalue problem for the transport equations. In this paper, we deal with the eigenvalue of the anisotropic scattering transport equation in slab geometry. We propose a new discrete method which was called modified discrete ordinates method. It is constructed by redeveloping and improving discrete ordinates method in the space of L1（X）. Different from traditional methods, norm convergence of operator approximation is proved theoretically. Furthermore, convergence of eigenvalue approximation and the corresponding error estimation are obtained by analytical tools.展开更多
基金Open Access funding provided by EPFL LausanneThe authors were supported in part by NSF grant DMS-17000282.
文摘We construct(modified)scattering operators for the Vlasov-Poisson system in three dimensions,mapping small asymptotic dynamics as t→−∞to asymptotic dynamics as t→+∞.The main novelty is the construction of modified wave operators,but we also obtain a new simple proof of modified scattering.Our analysis is guided by the Hamiltonian structure of the Vlasov-Poisson system.Via a pseudo-conformal inversion,we recast the question of asymptotic behavior in terms of local in time dynamics of a new equation with singular coefficients which is approximately integrated using a generating function.
基金Supported by the National Natural Science Foundation of China under Grant No.11405128Natural Science Basic Research Plan in Shaanxi Province of China under Grant No.15JK2093
文摘Within a Pekeris-type approximation to the centrifugal term, we examine the approximately analytical scattering state solutions of the l-wave Schrdinger equation with the modified Rosen–Morse potential. The calculation formula of phase shifts is derived, and the corresponding bound state energy levels are also obtained from the poles of the scattering amplitude.
基金supported in part by NSF(Grant No.DMS-1600028)NSF-FRG(Grant No.DMS-1463753)+1 种基金supported in part by NSF(Grant No.DMS-1362940)by a Sloan Research fellowship
文摘In this paper we consider a coupled Wave-Klein–Gordon system in 3 D, and prove global regularity and modified scattering for small and smooth initial data with suitable decay at infinity. This system was derived by Wang and LeFloch–Ma as a simplified model for the global nonlinear stability of the Minkowski space-time for self-gravitating massive fields.
文摘Some difficulties are pointed out in the methods for identification of obstacles based on the numerical verification of tile inclusion of a function in the range of an operator. Numerical examples are given to illustrate theoretical conclusions. Alternative methods of identification of obstacles are mentioned： the Support Function Method （SFM） and the Modified Rayleigh Conjecture （MRC） method.
基金The project supported by National Natural Science Foundation of China under Grant Nos.10371070 and 10671121the Foundation of Shanghai Education Committee for Shanghai Prospective Excellent Young Teachers
文摘This paper investigates in detail the dynamics of the modified KdV equation with self-consistent sources, including characteristics of one-soliton, scattering conditions and phase shifts of two solitons, degenerate case of two solitons and ＂ghost＂ solitons, etc. Co-moving coordinate frames are employed in asymptotic analysis.
基金Project(50735007) supported by the National Natural Science Foundation of ChinaProject(2010ZX04001-151) supported by Important National Science & Technology Specific Program of China
文摘To get the scattering loss of the trapezoidal core waveguide,a new analysis model is presented based on the perturbation equivalent method and modified effective-index method.Firstly,the trapezoidal core waveguide is successfully equivalent to the rectangular one with both restricting the same optical field energy by adopting the perturbation method,Then,the equivalent rectangular core waveguide is decomposed into two slab waveguides by employing the modified effective-index method,The trapezoidal core waveguide scattering theory model is established based on the slab waveguide scattering theory.With the sidewalls surface roughness in the range from 0 to 100 nm in the single model trapezodial core waveguide,optical simulation shows excellent agreement with the results from the scattering loss model presented.The relationship between the dimension and side-wall roughness with the scattering loss can be determined in the trapezoidal core waveguide by the scattering loss model.
文摘The small nanosilver was prepared by the sodium borohydride procedure. The aptamer was used to modify nanosilver to obtain a nanosilver-aptamer （AgssDNA） SERS probe for the determination of melamine. In pH 6.6 phosphate buffer solution and in the presence of NaCI, the AgssDNA probe specifically combined with melamine to release nanosilver particles that were aggregated to nanosilver clusters, which exhibited SERS effect at 240 cm-1. When melamine concentration increased, the nanosilver clusters increased, and the SERS intensity at 240 cm-1 in- creased. The increased SERS intensity AI240cm, is linear to melamine concentration in the range of 6.3--403.6 μg.L 1, with a detection limit of 1.2 μg L 1. This assay was applied to determination of melamine in milk, with sat- isfactory results. Keywords melamine, apatmer-modified nanosilver, aggregation, surface-enhanced Raman scattering
基金Supported by National Natural Science Foundation of China(Grant No.11201007)
文摘Criticality problem of nuclear tractors generMly refers to an eigenvalue problem for the transport equations. In this paper, we deal with the eigenvalue of the anisotropic scattering transport equation in slab geometry. We propose a new discrete method which was called modified discrete ordinates method. It is constructed by redeveloping and improving discrete ordinates method in the space of L1（X）. Different from traditional methods, norm convergence of operator approximation is proved theoretically. Furthermore, convergence of eigenvalue approximation and the corresponding error estimation are obtained by analytical tools.
